Exponential rings, exponential polynomials and exponential functions
type: Item
instance of: scholarly article
title: Exponential rings, exponential polynomials and exponential functions
zbMATH Open document ID: 0603.13019
published in: Pacific Journal of Mathematics
publication date: 1984-01-01T00:00:00Z
review text: An exponential ring is a pair (R,E), where R is a commutative ring with unit 1 and \(E: (R,+)\to U\) (the multiplicative group of units in R) satisfying \(E(x+y)=E(x)E(y)(x,y\in R),E(0)=1.\) In preparation for proving that each subset of \({\mathbb{R}}^ 2\) definable (with parameters) in the language of exponential rings has finitely many connected components, the author deals with the following questions. What is the structure of the free exponential rings and of the free algebras over a given exponential ring ? When is a map injective which assigns to a polynomial in \(x_ 1,...,x_ m\) over (R,E) the corresponding R-valued m-place function ?
Mathematics Subject Classification ID: 13L05
Mathematics Subject Classification ID: 03B25
Mathematics Subject Classification ID: 13B25
zbMATH DE Number: 3973019
zbMATH Keywords: decidability
zbMATH Keywords: free exponential rings
zbMATH Keywords: polynomial
author: Lou van den Dries
MaRDI profile type: Publication
full work available at URL: pjm.1984.113.51
OpenAlex ID: W2083789209
DOI: 10.2140/PJM.1984.113.51
description: scientific article; zbMATH DE number 3973019